Solve left(y-1right)^2+2(y-1)+2

$${ \left(y-1 \right) }^{ 2 } +2(y-1)+2$$

Evaluate

$$y^{2}+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.

$$y^{2}-2y+1+2\left(y-1\right)+2$$

Use the distributive property to multiply 2 by y-1.

$$y^{2}-2y+1+2y-2+2$$

Combine -2y and 2y to get 0.

$$y^{2}+1-2+2$$

Subtract 2 from 1 to get -1.

$$y^{2}-1+2$$

Add -1 and 2 to get 1.

$$y^{2}+1$$

Expand

$$y^{2}+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.

$$y^{2}-2y+1+2\left(y-1\right)+2$$

Use the distributive property to multiply 2 by y-1.

$$y^{2}-2y+1+2y-2+2$$

Combine -2y and 2y to get 0.

$$y^{2}+1-2+2$$

Subtract 2 from 1 to get -1.

$$y^{2}-1+2$$

Add -1 and 2 to get 1.

$$y^{2}+1$$